Answer:
Power = 377.35 W or Power = 0.5065 hp
Explanation:
Given:
Number of steps, n = 1576
height of each step, h = 0.20 m
Total height achieved, H = nh = 1576 × 0.20 = 315.2 m
Mass of the runner, M = 70.0 kg
Total time taken, t = 9 minutes 33 seconds = (9 × 60) + 33 = 573 seconds
Now, the potential energy gained by the runner,
E = MgH
where, g is the acceleration due to the gravity
on substituting the values in the above formula, we get
E = 70 × 9.8 × 315.2
or
E = 216227.2 J
also,
Energy = Power × time
therefore,
Power = Energy/time
or
Power = 216227.2 J / 573
or
Power = 377.35 W
Now,
745 watt = 1 hp
or
1 watt = 1/745 hp
thus,
Power = 377.35 W = 337.35 × (1/745) hp
or
Power = 0.5065 hp
The average power output during the climb is P= 377.35 in watts and P = 0.5065 in Horsepower
It is given that:
Number of steps, n = 1576
Height of each step, h = 0.20 m
So the total height will be calculated as
[tex]H=n\times h=1576\times 0.20=315.2m[/tex]
Mass of the runner M = 70.0 kg
Total time is taken to cover whole stairs
[tex]t=9 minutes 33seconds=(9\times60)+33=573seconds[/tex]
potential energy will be given as
[tex]E=M\times g\times H[/tex]
g is the acceleration due to gravity
By putting the values in the above formula
[tex]E=70\times 9.8\times315.2[/tex]
[tex]E=216227.2 J[/tex]
Now
[tex]Power= \dfrac{Energy}{Time}[/tex]
[tex]P=\dfrac{21622.2}{573}[/tex]
or
[tex]P=377.35W[/tex]
As we know that
[tex]745watt=1 hp[/tex]
or
[tex]1 watt=\dfrac{1}{745} hp[/tex]
So,
[tex]Power=377.35\times\dfrac{1}{745} hp[/tex]
[tex]Power=0.5065 hp[/tex]
Thus the average power output during the climb is P= 377.35 in watts and P = 0.5065 in Horsepower
To know more about Mechanical Power follow
https://brainly.com/question/24443465
